Question

In an A.C.circuit containing only capacitance, the current

• A. leads the voltage by $180^{\circ}$
• B. lags the voltage by $90^{\circ}$
• C. leads the voltage by $90^{\circ}$
• D. remains in phase with the voltage

Answer 1

Answer: (C)

leads the voltage by $90^{\circ}$

Answer 2

In a purely capacitive circuit, where there is no resistance, the current i flowing through it deposits a charge dq on the capacitor in time that is $dq = idt$ $\Rightarrow i=\frac{dq}{dt}$ Now using Kirchoff's law, if total charge deposited on the capacitor is $q$ then $\frac{q}{C}=E_{0} \sin \omega t$ $\Rightarrow q=C E_{0} \sin \omega t$ $\Rightarrow i=\frac{d q}{d t}=C E_{0} \omega \cos \omega t=i_{0} \cos \omega t$ where $i_{0}=\frac{E_{0}}{\left(1 / C_{\omega}\right)}$ = peak current $\therefore i=i_{0} \cos \omega t=i_{0} \sin \left(\omega+\frac{\pi}{2}\right) t$ and $E=E_{0} \sin \omega t$ Hence current is leading the voltage in phase by $\frac{\pi}{2}$